Answer
$$\frac{x^{2}}{2(x+4)}$$
Work Step by Step
The area of the smaller triangle A = $\frac{x(x+2)}{2}$
The area of the bigger triangle B = $\frac{(x+2)(x+4)}{x}$
The area of the shaded area = $B-A$
The area of the non-shaded area = $A$
The ratio between non-shaded area to shaded area = $\frac{A}{B-A}$=$\frac{\frac{x(x+2)}{2}}{\frac{(x+2)(x+4)}{x}}$= $\frac{\frac{x}{2}}{\frac{x+4}{x}}$=$\frac{x^{2}}{2(x+4)}$ (simplifying the complex fraction)
